P B Thomas and D Dhar 1994 J. Phys. A: Math. Gen. 27 2257 doi:10.1088/0305-4470/27/7/007
P B Thomas and D Dhar
Show affiliationsWe formulate the problem of determining the Hausdorf dimension, df, of the Apollonian packing of circles as an eigenvalue problem of a linear integral equation. We show that solving a finite-dimensional approximation to this infinite-order matrix equation and extrapolating the results provides a fast algorithm for obtaining high-precision numerical estimates for df. We find that df=1.305 686 729(10). This is consistent with the rigorously known bounds on df, and improves the precision of the existing estimate by three orders of magnitude.
45C05 Eigenvalue problems (See also 34Lxx, 35Pxx, 45P05, 47A75)
Issue 7 (7 April 1994)
P B Thomas and D Dhar 1994 J. Phys. A: Math. Gen. 27 2257
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